{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "655611fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Bayesian Linear Regression')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import BayesianRidge\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "warnings.filterwarnings((\"ignore\"))\n",
    "plt.style.use([\"classic\"])\n",
    "\n",
    "# 生成一些示例数据\n",
    "# np.random.seed(0)\n",
    "X = np.random.rand(100, 1)\n",
    "Y = 2 * X + 0.1*np.random.randn(100, 1)\n",
    "\n",
    "# 创建贝叶斯线性回归模型\n",
    "reg = BayesianRidge()\n",
    "\n",
    "# 拟合模型\n",
    "reg.fit(X, Y)\n",
    "\n",
    "# 预测新数据\n",
    "X_new = np.linspace(0, 1, 10).reshape(-1, 1)\n",
    "Y_pred, Y_std = reg.predict(X_new, return_std=True)\n",
    "\n",
    "# print(Y_pred.shape)\n",
    "# 计算95%的置信区间\n",
    "t_value = 1.96  # 95% 置信区间对应的 t 值\n",
    "\n",
    "confidence_interval = t_value * Y_std\n",
    "\n",
    "# 绘制观测数据和预测结果以及95%置信区间\n",
    "plt.scatter(X, Y, color='blue', label='Training data')\n",
    "plt.plot(X_new, Y_pred, color='red', linewidth=2, label='Predicted data')\n",
    "plt.fill_between(X_new.ravel(), (Y_pred - confidence_interval).ravel(), (Y_pred + confidence_interval).ravel(), color='pink', alpha=0.3, label='95% Confidence Interval')\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend(loc = \"upper left\")\n",
    "plt.title('Bayesian Linear Regression')\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2d3d6de4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
